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engineering
engineering mechanics statics

Engineering Mechanics Statics & Dynamics 15th Edition Russell C. Hibbeler - Solutions

The wheel has a mass of 100 kg and a radius of gyration of kO = 0.2 m. A motor supplies a torque M = (40θ + 900) N · m, where θ is in radians, about the drive shaft at O. Determine the speed of the loading car, which has a mass of 300 kg, after it travels s = 4 m. Initially the car is at rest
The coefficient of kinetic friction between the 100-lb disk and the surface of the conveyor belt is μA = 0.2. If the conveyor belt is moving with a speed of vC = 6 ft/s when the disk is placed in contact with it, determine the number of revolutions the disk makes before it reaches a constant
If corner A of the 60-kg plate is subjected to a vertical force of P = 500 N, and the plate is released from rest when θ = 0°, determine the angular velocity of the plate when θ = 45°. A P = 500 N 0 1 m. B 1m
When a force of P = 30 lb is applied to the brake arm, the 50-lb cylinder A is descending with a speed of 20 ft/s. Determine the number of revolutions wheel B will rotate before it is brought to a stop. The coefficient of kinetic friction between the brake pad C and the wheel is μk = 0.5. The
If the 50-lb bucket C is released from rest, determine its velocity after it has fallen a distance of 10 ft. The windlass A can be considered as a 30-lb cylinder, while the spokes are slender rods, each having a weight of 2 lb. Neglect the pulley’s weight. B C -3 ft- - 0.5 ft. A 00 4 ft 0.5
A uniform ladder having a weight of 30 lb is released from rest when it is in the vertical position. If it is allowed to fall freely, determine the angle θ at which the bottom end A starts to lift off the ground. For the calculation, assume the ladder to be a slender rod and neglect friction at A.
The link AB is subjected to a couple moment of M = 40 N · m. If the ring gear C is fixed, determine the angular velocity of the 15-kg inner gear when the link has made two revolutions starting from rest. Neglect the mass of the link and assume the inner gear is a disk. Motion occurs in the
The 50-1b cylinder A is descending with a speed of 20 ft/s when the brake is applied. If wheel B must be brought to a stop after it has rotated 5 revolutions, determine the constant force P that must be applied to the brake arm. The coefficient of kinetic friction between the brake pad C and the
A ball of mass m and radius r is cast onto the horizontal surface such that it rolls without slipping. Determine the minimum speed vG of its mass center G so that it rolls completely around the loop of radius R + r without leaving the track. VG OR
The 10-kg rod AB is pin connected at A and subjected to a couple moment of M = 15 N · m. If the rod is released from rest when the spring is unstretched at θ = 30°, determine the rod’s angular velocity at the instant θ = 60°. As the rod rotates, the spring always remains horizontal, because
The two 2-kg gears A and B are attached to the ends of a 3-kg slender bar. The gears roll within the fixed ring gear C, which lies in the horizontal plane. If a 10 · N m torque isapplied to the center of the bar as shown, determine thenumber of revolutions the bar must rotate starting from restin
Gears C and H each have a weight of 0.4 lb and a radius of gyration about their mass center of kA = kB = 2 in. The uniform link AB has a weight of 0.2 lb and a radius of gyration of kA = 3 in., whereas link DE has a weight of 0.15 lb and a radius of gyration of kB = 4.5 in. If a couple moment M = 3
Motor M exerts a constant force of P = 750 N on the rope. If the 100-kg post is at rest when θ = 0°, determine the angular velocity of the post at the instant θ = 60°. Neglect the mass of the pulley and its size, and consider the post as a slender rod. M P= 750 N C B 3 m A 4 m
The spool has a mass of 100 kg and a radius of gyration of 400 mm about its center of mass O. If it is released from rest, determine its angular velocity after its center O has moved down the plane a distance of 2 m.The coefficient of kinetic friction between the spool and the inclined plane is μk
A ball of mass m and radius r is cast onto the horizontal surface such that it rolls without slipping. Determine its angular velocity at the instant θ = 90°, if it has an initial speed of vG as shown. VG. out R
The spool has a mass of 100 kg and a radius of gyration of 400 mm about its center of mass O.If it is released from rest, determine its angular velocity after its center O has moved down the plane a distance of 2 m. The contact surface between the spool and the inclined plane is smooth. 600
A chain that has a negligible mass is draped over the sprocket which has a mass of 2 kg and a radius of gyration of ko = 50 mm. If the 4-kg block A is released from rest from the position s = 1 m, determine the angular velocity of the sprocket at the instant s = 2 m. 100 mm- s = 1 m A 0
The assembly consists of a 3-kg pulley A and 10-kg pulley B. If a 2-kg block is suspended from the cord, determine the block’s speed after it descends 0.5 m starting from rest. Neglect the mass of the cord and treat the pulleys as thin disks. No slipping occurs. B 100 mm 30 mm A
The 6-kg rod ABC is connected to the 3-kg rod CD. If the system is released from rest when θ = 0°, determine the angular velocity of rod ABC at the instant it becomes horizontal. A 0.5 m B D 0 0.3 m C 0.4 m
The assembly consists of a 3-kg pulley A and 10-kg pulley B. If a 2-kg block is suspended from the cord, determine the distance the block must descend, starting from rest, in order to cause B to have an angular velocity of 6 rad/s. Neglect the mass of the cord and treat the pulleys as thin disks.
The 25-lb slender rod AB is attached to spring BC which has an unstretched length of 4 ft. If the rod is released from rest when θ = 30°, determine its angular velocity at the instant θ = 90°. C 4 ft k = 5 lb/ft 4 ft B
The 25-lb slender rod AB is attached to spring BC which has an unstretched length of 4 ft. If the rod is released from rest when θ = 30°, determine the angular velocity of the rod the instant the spring becomes unstretched. C 4 ft k = 5 lb/ft 4 ft B
Solve Prob. 18–38 if the chain has a mass of 0.8 kg/m. For the calculation neglect the portion of the chain that wraps over the sprocket.Solve Prob. 18–38A chain that has a negligible mass is draped over the sprocket which has a mass of 2 kg and a radius of gyration of ko = 50 mm. If the 4-kg
The two bars are released from rest at the position θ = 90°. B Determine their angular velocities at the instant they become horizontal. Neglect the mass of the roller at C. Each bar has a mass m and length L. A O L B L DE C
The tire has a mass of 8 kg a radius of 0.3 m and a radius of gyration about its center of gravity G of kG = 0.25 m. If it is released from rest at the top of the hill, determine the velocity of its center at the bottom of the hill if it rolls without slipping. 4 m A B
The uniform 150-lb stone (rectangular block) is being turned over on its side by pulling the vertical cable slowly upward until the stone begins to tip. If it then falls freely (T = 0) from an essentially balanced at-rest position, determine the speed at which the corner A strikes the pad at
The assembly consists of two 8-lb bars which are pin connected to the two 10-lb disks. If the bars are released from rest when θ = 60°, determine their angular velocities at the instant θ = 30°. Assume the disks roll without slipping. 0.5 ft 3 ft B 3 ft 0.5 ft
The two bars are released from rest at the position θ. Determine their angular velocities at the instant they become horizontal. Neglect the mass of the roller at C. Each bar has a mass m and length L. A L B Ꮎ 0 L C
The pavement compactor is traveling down the incline at vG = 5 ft/s when the motor is disengaged. Determine the angular velocity of the roller B when the compactor has traveled 20 ft down the plane. The body of the compactor, excluding the rollers, has a weight of 8000 lb and a center of gravity at
The 40-kg wheel has a radius of gyration about its center of gravity G of kG = 250 mm. If it rolls without slipping, determine its angular velocity when it has rotated clockwise 90° from the position shown. The spring AB has a stiffness k = 100 N/m and an unstretched length of 500 mm. The wheel is
If the 250-lb block is released from rest when the spring is unstretched, determine the velocity of the block after it has descended 5 ft.The drum has a weight of 50 lb and a radius of gyration of kO = 0.5 ft about its center of mass O. k = 75 lb/ft M 0.375 ft 0.75 ft
The uniform garage door has a mass of 150 kg and is guided along smooth tracks at its ends. Lifting is done using the two springs, which are attached to the anchor bracket at A and to the counterbalance shaft at B and C. As the door is raised, the springs begin to unwind from the shaft, thereby
The pendulum of the Charpy impact machine has a mass of 50 kg and a radius of gyration of kA = 1.75 m. If it is released from rest when θ = 0°, determine its angular velocity just before it strikes the specimen S, θ = 90°. 1.25 m
The two 12-kg slender rods are pin connected and released from rest at the position θ = 60°. If the spring has an unstretched length of 1.5 m, determine the angular velocity of rod BC, when the system is at the position θ = 0°. Neglect the mass of the roller at C. A 2 m B k = 20 N/m 2 m C
A large roll of paper having a mass of 20 kg and a radius r = 150 mm is resting over the edge of a corner, such that the end of the paper on the roll is attached to the horizontal surface. If the roll is disturbed slightly from its equilibrium position, determine the angle θ at which it begins to
At a given instant the body of mass m has an angular velocity ω and its mass center has a velocity vG. Show that its kinetic energy can be represented as T = 1/2IICω2, where IIC is the moment of inertia of the body determined about the instantaneous axis of zero velocity, located a distance
The 50-kg flywheel has a radius of gyration of kO = 200 mm about its center of mass. If it is subjected to a torque of M = (9θ¹/2+1) N-m, where θ is in radians, determine its angular velocity when it has rotated 5 revolutions, starting from rest. M = (9 0¹2 + 1) N-m
The slender 15-kg bar is initially at rest and standing in the vertical position when the bottom end A is displaced slightly to the right. If the track in which it moves is smooth, determine the speed at which end A strikes the corner D. The bar is constrained to move in the vertical plane. Neglect
The uniform 50-lb slender rod is subjected to a couple moment of M = 100 lb ft. If the rod is at rest when θ = 0°, determine its angular velocity when θ = 90°. O M=100 lb-ft 5 ft
The 80-kg wheel has a radius of gyration about its mass center O of ko = 400 mm. Determine its angular velocity after it has rotated 20 revolutions starting from rest. 0.6 m P = 50 N
Each gear has mass of 2 kg and a radius of gyration about its pinned mass center A or B, respectively of kg = 40 mm. Each link has a mass of 2 kg and a radius of gyration about its pinned end A or B, of k∫ = 50 mm. If originally the spring is unstretched when the couple moment M = 20N · m is
The spool has a mass of 60 kg and a radius of gyration kG = 0.3 m. If it is released from rest, determine how far its center descends down the smooth plane before it attains an angular velocity of ω = 6 rad/s. Neglect friction and the mass of the cord which is wound around the central core. 0.3
The uniform 50-kg slender rod is at rest in the positionshown when P = 600 N is applied. Determine the angularvelocity of the rod when the rod reaches the vertical position. 4 m 5 m P = 600 N B
The spool has a mass of 40 kg and a radius of gyration of kO = 0.3 m. If the 10-kg block is released from rest, determine the distance the block must fall in order for the spool to have an angular velocity ω = 15 rad/s. Also, what is the tension in the cord while the block is in motion? Neglect
The drum has a mass of 50 kg and a radius of gyration about the pin at O of kO = 0.23 m. Starting from rest, the suspended 15-kg block B is allowed to fall 3 m without applying the brake ACD. Determine the speed of the block at this instant. If the coefficient of kinetic friction at the brake pad C
Solve Prob. 18–2 if the coefficient of kinetic friction between the spool and plane at A is μk = 0.2.Solve Prob. 18–2The spool has a mass of 60 kg and a radius of gyration kG = 0.3 m .If it is released from rest, determine how far its center descends down the smooth plane before it attains an
The gear rack has a mass of 6 kg, and the gears each have a mass of 4 kg and a radius of gyration of k = 30 mm at their centers. If the rack is originally moving downward at 2 m/s, when s = 0, determine the speed rack when s = 600 mm. The gears are free to turn about their centers A and B. 50
The 50-kg wheel is subjected to a force of 50 N. If the wheel starts from rest and rolls without slipping, determine its angular velocity after it has rotated 10 revolutions. The radius of gyration of the wheel about its mass center G is kG = 0.3 m. P = 50 N 30% 4 0.4 m
The spool weighs 20 lb and has a radius of gyration of kG = 3 in. If it is released from rest, determine how far it must drop before the velocity of its center becomes 20 ft/s. The cable is wrapped around the inner hub of the spool and unravels as the spool rotates. Neglect the mass of the cable. 4
If the uniform 30-kg slender rod starts from rest at the position shown, determine its angular velocity after it has rotated 4 revolutions. The forces remain perpendicular to the rod. 30 N 10.5 m 0.5 m 0 1.5 m- 20 N-m 10.5 m 20 N
A force of P = 20 N is applied to the cable, which causes the 175-kg reel to turn since it is resting on the two rollers A and B of the dispenser. Determine the angular velocity of the reel after it has made two revolutions starting from rest. Neglect the mass of the rollers and the mass of the
The compound disk pulley consists of a hub and attached outer rim. If it has a mass of 3 kg and a radius of gyration of kG = 45 mm, determine the speed of block A after A descends 0.2 m from rest. Blocks A and B each have a mass of 2 kg. Neglect the mass of the cords. 30 mm- B 100 mm A
A force of P = 20 N is applied to the cable, which causes the 175-kg reel to turn without slipping on the two rollers A and B of the dispenser. Determine the angular velocity of the reel after it has made two revolutions starting from rest. Neglect the mass of the cable. Each roller can be
The 20-kg wheel has a radius of gyration about its center G of kG = 300 mm. When it is subjected to a couple moment of M = 50 N · m, it rolls without slipping. Determine the angular velocity of the wheel after its mass center G has traveled through a distance of sG = 20 m, starting from rest. M =
The system consists of a 20-lb disk A, 4-lb slender rod BC, and a 1-lb smooth collar C. If the disk rolls without slipping, determine the velocity of the collar at the instant the rod becomes horizontal, i.e., θ = 0°. The system isreleased from rest when θ = 45°. B 0.8 ft 3 ft A C
If the 30-kg disk is released from rest when θ = 0°,determine its angular velocity when θ = 90°. Jo G 0.3 m
The double pulley consists of two parts that are attached to one another. It has a weight of 50 lb and a radius of gyration about its center of kO = 0.6 ft and is turning with an angular velocity of 20 rad/s clockwise. Determine the kinetic energy of the system. Assume that neither cable slips on
At the instant the spring becomes undeformed, the center of the 40-kg disk has a speed of 4 m/s. From this point determine the distance d the disk moves down the plane before momentarily stopping. The disk rolls without slipping. k = 200 N/m www 0.3 m 30°
The 60-kg rod OA is released from rest when θ = 0°. Determine its angular velocity when θ = 45°. The spring remains vertical during the motion and is unstretched when θ = 0°. 3 m k = 150 N/m
The 50-kg reel has a radius of gyration about its center G of kG = 300 mm. If it is released from rest, determine its angular velocity when its center G has traveled 6 m down the smooth inclined plane. 0.2 m 30° G 0.4 m
The double pulley consists of two parts that are attached to one another. It has a weight of 50 lb and a centroidal radius of gyration of kO = 0.6 ft and is turning with an angular velocity of 20 rad s clockwise. Determine the angular velocity of the pulley at the instant the 20-lb weight moves 2
The 30-kg rod is released from rest when θ = 0°.Determine the angular velocity of the rod when θ = 90°.The spring is unstretched when θ = 0°. 1.5 m -2 m- wwwwwwww k = 80 N/m
The disk, which has a mass of 20 kg, is subjected to the couple moment of M = (2θ + 4) N · m, where θ is in radians. If it starts from rest, determine its angular velocity when it has made two revolutions. 300 mm M
A motor delivers 50 lb · ft of torque to the pinion gear D, which is in mesh with the larger gear A and the attached drum over which the cable winds. If A has a weight of 120 lb and a radius of gyration kA = 0.6 ft, determine the velocity of the 50-lb crate C when it has risen 5 ft starting from
The 30-kg rod is released from rest when θ = 45°. Determine the angular velocity of the rod when θ = 0°. The spring is unstretched when θ = 45°. B 1.5 m k = 300 N/m A
The revolving door consists of four doors which are attached to an axle AB. Each door can be assumed to be a 50-lb thin plate. Friction at the axle contributes a moment of 2 lb · ft which resists the rotation of the doors. If a women passes through one door by always pushing with a force P = 15 lb
The 20-kg rod is released from rest when θ = 0°. Determine its angular velocity when θ = 90°. The spring has an unstretched length of 0.5 m. A W 2m -2m- B 1 m k = 100 N/m
The 10-kg uniform slender rod is suspended at rest from the pin at 0 when the force of F = 150 N is applied to its end. Determine the angular velocity of the rod when it has rotated 90° clockwise from the position shown. The force is always perpendicular to the rod. 3 m O F
The 10-kg uniform slender rod is suspended at rest from the pin at O when the force of F = 150 N is applied to its end. Determine the angular velocity of the rod when it has rotated 180° clockwise from the position shown. The force is always perpendicular to the rod. 3 m F
The pendulum consists of a 10-kg uniform disk and a 3-kg uniform slender rod. If it is released from rest in the position shown, determine its angular velocity when it rotates clockwise 90°. M = 30 N·m 2 m B 0.8 m
The small gear has a mass m and may be treated as a uniform disk. If it is released from rest at θ = 0°, and rolls along the fixed circular gear rack, determine the angular velocity of the radial line AB at the instant θ = 90°. m R ขนา A B แบบใหม่
The slender rod has a mass of 10 kg and is released from rest when it is in the vertical position. Determine its angular velocity at the instant it becomes horizontal. The attached block at D has a mass of 4 kg. The mass of the cable and pulley at C can be neglected. B 2 m A 3 m- D
The uniform rectangular door panel has a mass of 25 kg and is held in equilibrium above the horizontal at the position θ = 60° by rod BC. Determine the required stiffness of the torsional spring at A, so that the door's angular velocity becomes zero when the door reaches the closed position (θ =
The arm and seat of the amusement-park ride have a mass of 1.5 Mg, with the center of mass located at point G1. The passenger seated at A has a mass of 125 kg, with the center of mass located at G2. If the arm is raised to a position where θ = 150° and released from rest, determine the speed of
The uniform bar AB has a mass of 12 kg and is pin connected at A. If the support at B is remove (θ = 90°), determine the velocity of the 5-kg block C at the instant the bar rotates downward to θ = 150°. Neglect the size and mass of the pulley at D. A -1 m Bo C D 1 m 1.5 m
Pulley A has a weight of 30 lb and a centroidal radius of gyration kB = 0.6 ft. Determine the speed of the 20-lb crate C at the instant s = 10 ft. Initially, the crate is released from rest when s = 5 ft. The pulley at P "rolls" downward on the cord without slipping. For the calculation, neglect
The 50-lb wheel has a radius of gyration about its center of gravity G of KG = 0.7 ft. If it rolls without slipping, determine its angular velocity when it has rotated clockwise 90° from the position shown. The spring AB has a stiffness k = 1.20 lb/ft and an unstretched length of 0.5 ft. The wheel
The system consists of 60-lb and 20-lb blocks A and B, respectively, and 5-lb pulleys C and D that can be treated as thin disks. Determine the speed of block A after block B has risen 5 ft, starting from rest. Assume that the cord does not slip on the pulleys, and neglect the mass of the
Gear A has a mass of 0.5 kg and a radius of gyration of kA = 40 mm, and gear B has a mass of 0.8 kg and a radius of gyration of kB = 55 mm. The link is pinned at C and has a mass of 0.35 kg. If the link can be treated as a slender rod, determine the angular velocity of the rod after the assembly is
The gear is pinned at A and has a mass of 0.3 kg and a radius of gyration of kA = 25 mm. The gear rack has mass of 0.5 kg. If has spring is stretched 50 mm and released from rest, determine the angular velocity of the gear at the instant the spring compresses 20 mm. Neglect friction. 50 mm m ω k =
Determine the moment of inertia Iz of the frustum of the cone, which has a conical depression. The material has a density of 200 kg/m3. 200 mm- 800 mm Z 600 mm 400 mm
The pendulum consists of a plate having a weight of 12 lb and a slender rod having a weight of 4 lb. Determine the radius of gyration of the pendulum about an axis perpendicular to the page and passing through point O. 1 1 ft I |--10--- -1 ft- 3 ft -2 ft-
The pendulum consists of a 2-kg disk, and slender rods AB and DC which have a mass per unit length of 2 kg/m. Determine the length L of DC so that the center of mass is at the bearing O. What is the moment of inertia of this assembly about an axis perpendicular to the page and passing through point
The jet plane has a mass of 250 Mg and a horizontal velocity of 100 m/s when t = 0. If both engines provide a horizontal thrust which varies as shown in the graph, determine the plane’s velocity in t = 5 s. Neglect air resistance and the loss of fuel during the motion. F(KN) ******** F = 200 +
Determine the moment of inertia Iy for the slender rod. The rod’s density ρ and cross-sectional area A are constant. Express the result in terms of the rod’s total mass m. N
The handcart has a mass of 200 kg and center of mass at G. Determine the normal reactions at each of the wheels at A and B if a force P = 50 N is applied to the handle. Neglect the mass and rolling resistance of the wheels. A 0.3 m B ¹0.2 m 0.2 m 0.4 m- P 60° 0.5 m
The two 3-lb rods EF and HI are fixed (welded) to the link AC at E. Determine the internal axial force Ex shear force Ey, and moment ME, which the bar AC exerts on FE at E if at the instant θ = 30° link AB has an angular velocity ω = 5 rad/s and an angular acceleration α = 8 rad/s²as shown. 2
The cart and its load have a total mass of 100 kg. Determine the acceleration of the cart and the normal reactions on the pair of wheels at A and B. Neglect the mass of the wheels. 100 N 1.2 m OB 0.3 m 0.4 m 0.6 m A 0.5 m
The solid cylinder has an outer radius R, height h, and is made from a material having a density that varies from its center as ρ = k + ar2, where k and a are constants. Determine the mass of the cylinder and its moment of inertia about the z axis. N R h
The 20-lb link AB is pinned to a moving frame at Aand held in a vertical position by means of a string BC whichcan support a maximum tension of 10 lb. Determine themaximum acceleration of the frame without breaking thestring. What are the corresponding components of reactionat the pin A? T 3 ft 4
If the 80-kg cabinet is allowed to roll down theinclined plane, determine the acceleration of the cabinetand the normal reactions on the pair of rollers at A and Bthat have negligible mass. 1.5 m B G 0.5 m 0.5 m 115°
Determine the moment of inertia of the thin ring about the z axis.The ring has a mass m. y R -X
A 20-kg roll of paper, originally at rest, is pin supported at its ends to bracket AB. The roll rests against a wall for which the coefficient of kinetic friction at C is μc=0.3. If a force of 40 N is applied uniformly to the end of the sheet, determine the initial angular acceleration of the roll
The car has a mass of 1.50 Mg and a mass center at G. Determine the maximum acceleration it can have if power is supplied only to the rear wheels. Neglect the mass of the wheels in the calculation, and assume that the wheels that do not receive power are free to roll. Also, assume that slipping of
At the instant shown both rods of negligible mass swing with a counterclockwise angular velocity of ω = 5 rad/s, while the 50-kg bar is subjected to the 100-N horizontal force. Determine the tension developed in the rods and the angular acceleration of the rods at this instant. 1.5 m 100 N A- w =
Determine the maximum acceleration of the truck without causing the 100-kg assembly to move relative to the truck. Also what is the corresponding normal reaction on legs A and B? The assembly has a mass center at G and the coefficient of static friction between its legs and the truck bed is μs =
The right circular cone is formed by revolving the shaded area around the x axis. Determine the moment of inertia Ix and express the result in terms of the total mass m of the cone. The cone has a constant density ρ. y = 7x h -h- r X
At the instant shown, two forces act on the 30-lb slender rod which is pinned at O. Determine the magnitude of force F and the initial angular acceleration of the rod so that the horizontal reaction which the pin exerts on the rod is 5 lb directed to the right. 3 ft 3 ft +s4 2 ft 0 - F 20 lb
Determine the mass moment of inertia Iz of the cone formed by revolving the shaded area around the z axis. The total density of the material is ρ. Express the results in terms of the mass m of the cone. X Z = 4 (r-y) Z= h
The pendulum consists of a 30-lb sphere and a 10-lb slender rod. Compute the reaction at the pin O just after the cord AB is cut. 1 ft B 2 ft

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